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Confidence bounds when the estimated ROC area is 1.01
Nancy A Obuchowski1, Michael L Lieber
1Department of Biostatistics and Epidemiology The Cleveland Clinic Foundation, 9500 Euclid Avenue, Cleveland OH, 44195, USA.
Academic Radiology
|December 3, 2002
Summary
When the estimated area under the receiver operating characteristic (ROC) curve is 1.0, standard methods fail to provide confidence bounds. This study develops tables for approximate 95% lower confidence bounds in such cases.
Area of Science:
- Biostatistics
- Medical Diagnostics
Background:
- Small sample sizes in studies can lead to an estimated area under the receiver operating characteristic (ROC) curve of 1.0.
- Traditional methods for calculating standard errors and confidence bounds are inadequate when the ROC area is 1.0.
Purpose of the Study:
- To develop tables for determining the approximate 95% lower confidence bound for the area under the ROC curve when the estimated value is 1.0.
Main Methods:
- Monte Carlo simulations were used to generate 10,000 datasets for various sample sizes, ROC curve shapes, and data formats (continuous and ordinal).
- The 95% lower confidence bound was determined for each simulated combination.
Main Results:
- The 95% lower confidence bounds varied significantly based on ROC curve shape and data format (ordinal vs. continuous).
- Four tables of 95% lower confidence bounds are presented with usage guidelines.
Conclusions:
- A single, universally applicable method for constructing confidence bounds for all ROC curves is not feasible due to variations in curve shapes and data collection formats.
- The provided tables offer a practical tool for interpreting studies where the estimated ROC area is 1.0.